Re: FindInstance question? Any ideas to solve this equality.

*To*: mathgroup at smc.vnet.net*Subject*: [mg128568] Re: FindInstance question? Any ideas to solve this equality.*From*: Dana DeLouis <dana01 at me.com>*Date*: Sun, 4 Nov 2012 20:12:12 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

Hi. I might hold off inserting machine numbers until later. Here's one idea: data={ radiusV1->145.98630072715727, radiusV2->95.62128455180272, slopeV1Deg->9.462322208025617, slopeV2Deg->18.43494882292201 }; Work with your equation. (I'll use t1 & t2) (360*radiusV1)/(slopeV1Deg+360*timeV1x)==(360*radiusV2)/(slopeV2Deg+360*timeV2x)&&(360*(radiusV1*2))/(slopeV1Deg*2+360*(timeV1x*2))==(360*(radiusV2*2))/(slopeV2Deg*2+360*(timeV2x*2)) /. {timeV1x->t1,timeV2x->t2} ; I find this easier to work with this: equ = %//FullSimplify radiusV1/(slopeV1Deg+360 t1)==radiusV2/(slopeV2Deg+360 t2) Let's solve for t1: FullSimplify[Solve[equ,t1]] [[1,1,-1]] (-radiusV2 slopeV1Deg+radiusV1 (slopeV2Deg+360 t2))/(360 radiusV2) Now, use your data: %/.data // FullSimplify 0.051896 +1.52671 t2 So, t1 is equal to the above. If we subtract them, the equation is equal to zero. t1-% -0.051896+t1-1.52671 t2 f equals the above equation that is equal to zero. f=% -0.051896+t1-1.52671 t2 There really is no integer solution within a large range: Minimize[{Abs[f],0<t1<10000000000,0<t2<10000000000},{t1,t2},Integers] {0.578609,{t1->1,t2->1}} As a side note: If you Rationalized the machine numbers, you would have: Rationalize[f,0] -(3592760/69229991)+t1-(118038537 t2)/77315450 Try to use integers for t1 & t2 %*77315450 //FullSimplify -(277775856142000/69229991)+77315450 t1-118038537 t2 Rearranged, you would have: 77315450 t1-118038537 t2 == 277775856142000 / 69229991 As you can see, there are no integer solutions for t1 & t2 that would give a rational number. Even if you wanted to round the rational number, the solution is still not reasonable: 277775856142000 / 69229991 // Floor 4012363 Minimize[Abs[77315450 t1-118038537 t2-4012363],{t1,t2},Integers] {0,{t1->471271145234969,t2->308683431630951}} Minimize[Abs[77315450 t1-118038537 t2-4012364],{t1,t2},Integers] {0,{t1->471271262689732,t2->308683508564028}} Just throwing this out. You may find the function FrobeniusSolve and related functions interesting reading. However, it doesn't help here for this problem. = = = = = = = = = = HTH :>) Dana DeLouis Mac & Mathematica 8 = = = = = = = = = = On Friday, November 2, 2012 11:54:28 PM UTC-4, Lea Rebanks wrote: > FindInstance question: > Hi All, > I have evaluated the following equality with FindInstance function and > > there appears to be no results. > > Please could someone review the following equality to see if my result is > > TRUE or Is it possible to find one or more Integer results to this equality. > Clear[radiusV1] > > radiusV1 = 145.98630072715727; > Clear[radiusV2] > radiusV2 = 95.62128455180272; > Clear[slopeV1Deg] > slopeV1Deg = 9.462322208025617; > Clear[slopeV2Deg] > > slopeV2Deg = 18.43494882292201; > > Clear[timeV1x] > > Clear[timeV2x] > > FindInstance[(360*radiusV1)/(slopeV1Deg + 360*timeV1x) == > (360*radiusV2)/(slopeV2Deg + 360*timeV2x) && > > (360*(radiusV1*2))/(slopeV1Deg*2 + 360*(timeV1x*2)) == > > (360*(radiusV2*2))/(slopeV2Deg*2 + 360*(timeV2x*2)) && > > timeV1x > 0 && timeV2x > 0, {timeV1x, timeV2x}, > > Integers, 2] > > {} > > > Any help or advice gratefully received. > > Best regards, > > Lea=85